CHICAGO — United Airlines faced an employee relations nightmare Sunday because of unresolved issues, most notably the failure to fashion an orderly back-to-work agreement for 10,000 flight attendants after pilots agreed to end a strike.

The nation's largest airline will unveil fare reductions today aimed at recapturing consumer loyalty lost in the 29-day walkout by pilots, whose picket lines were honored by most flight attendants.

On Sunday, United flew at 14 percent of its normal schedule, the same as during the walkout. It will begin adding flights Thursday and expects to have 40 percent of its regular schedule in place by June 25 and 100 percent in early July.

But as it seeks to win the hearts and dollars of travelers, it faces certain hostility from attendants as well as pilots hired during the walkout. Although some major pilot issues remain, the company and the Air Line Pilots Association reached a back-to-work agreement. It assures that striking pilots return to their pre-strike assignments.

No such accord was reached with the Association of Flight Attendants. The prime obstacle was disagreement over seniority of attendants who crossed the picket lines and those who didn't. Also, there was no agreement on working attendants who transferred to better routes.

Seniority is crucial to attendants, who bid each month for routes based on how long they have been with the company. Officials of the company and union usually devise the next month's ''lines of flying.''

A line of flying is a set of trips for which attendants bid. For example, one line might consist of three days of flights to and from Chicago, Boston, Baltimore, Philadelphia and Denver, including layovers.

Each month attendants receive a list of lines scheduled for the next month. They fill out cards with preferences and their seniority levels. A computer figures who wins the right to trips based on seniority.

Confusion is expected when bidding takes place for July unless the two sides can agree. United says the strikers have forfeited 29 days of seniority, and the union says they are due an accrual.

If United sticks to its position, many strikers would lose out to non- strikers in bidding, meaning some strikers would be placed on ''reserve'' and wouldn't work.